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Combinatorica

, Volume 38, Issue 5, pp 1149–1174 | Cite as

Essential Dimension and the Flats Spanned by a Point Set

  • Ben Lund
Original Paper
  • 23 Downloads

Abstract

Let P be a finite set of points in ℝd or ℂd.We answer a question of Purdy on the conditions under which the number of hyperplanes spanned by P is at least the number of (d−2)-flats spanned by P.

In answering this question, we define a new measure of the degeneracy of a point set with respect to affine subspaces, termed the essential dimension. We use the essential dimension to give an asymptotic expression for the number of k-flats spanned by P, for 1≤kd−1.

Mathematics Subject Classification (2000)

52C10 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA

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